Which of the following numbers is a multiple of 7? ${51,61,70,75,115}$
Explanation: The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $51 \div 7 = 7\text{ R }2$ $61 \div 7 = 8\text{ R }5$ $70 \div 7 = 10$ $75 \div 7 = 10\text{ R }5$ $115 \div 7 = 16\text{ R }3$ The only answer choice that leaves no remainder after the division is $70$ $ 10$ $7$ $70$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $70$ $70 = 2\times5\times7 7 = 7$ Therefore the only multiple of $7$ out of our choices is $70$. We can say that $70$ is divisible by $7$.